What is
Correlation between Age and Blindness

Example:The following table gives the distribution of the total population and those who are totally or partially blind among them. Find out if there is any correlation between age and blindness:

Age :

0—10

10—20

20—30

30—40

40—50

50-60

60—70

70-80

No. of

persons

(in '000)

100

60

40

36

24

11

6

3

Blind

55

40

40

40

36

22

18

(Bhagalpur Univ., 1979)

Solution: Here the class-interval of age will be represented by its mid-value and the per lakh, per thousand or per 100 of blind persons out of the total number in a particular group will be calculated. We shall calculate the number of blind persons out of 1 lakh in each group. Thus the class-interval 0—10 would be represented by 5 and blind

per lakh would be 55/(1,00,00 ) × 1, 00,000 = 55 in 10 – 50 group

40/60,000 × 1, 00,000 = 67 and so on.

Age Group

X

Mid values.

(m.v.)

Dev. From assumed av.45

(dx)/i

dx/i2

Blind per lakh.

Y

Dev. From assumed av. 80

dy

dy2

dxdy

0-10

5

-4

16

55

-125

15,625

+500

10-20

15

-3

9

67

-113

12,769

+339

20-30

25

-2

4

100

-80

6,400

+160

30-40

35

-1

1

111

-69

4,761

+69

40-50

45

0

0

150

-30

900

0

50-60

55

+1

1

200

+20

400

+20

60+70

65

+2

4

300

+120

14,400

+240

70-80

75

+3

9

500

+320

1,02,400

+260

n = 8

∑dx/i = -4

∑(dx/i)2

= 44

∑dy = +53

∑dy2 = 1,57,655

∑dxdy = 2,288

Calculation of Coefficient of Correlation

Note. We have taken step-deviations in X—series. As has been pointed out in an earlier question, this

does not affect the value of r and no adjustment is needed for it

r = ((∑dxdy-(∑dx)(∑dy))/n)/(√(∑dx2-(∑dx)2/n) √(∑dx2-(∑dx)2/n)

= (2,228-((-4) (+53))/10)/(√(44-(-4)2/8) √(1,57,655-(+53)2/8))

= (2.228+26.5)/√((44-2)(1,57,655-351.125))=2314.5/√(42×1,57,030.875)

= A.L. [log2314.5 1/2 (log42+log.1,57,303.875]

= A.L. [3.3644-1/2 (1.6232+5.1967) ]

= A.L. (3.3644 – 3.4099 = A.L. (1.9544) = + 0.899

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